Question

If the tension in the stretched string is increased by 69%, its fundamental frequency ______.

Options

• decreases by 30%

• increases by 30%

• increases by 69% 

• increases by 23%

Answer 1

If the tension in the stretched string is increased by 69%, its fundamental frequency increases by 30%.

Explanation:

∵ T₂ = T₁ + 69% of T₁ = 1.69 T₁

⇒ `T_2/T_1 = 1.69 = 169/100`

The fundamental frequency of a stretched string,

`f = 1/(2pi)sqrt(T/l)`

= `f ∝ sqrtT ⇒ f_2/f_1 = sqrt(T_2/T_1) = sqrt(169/100) = 13/10`

∵ % increase in frequency = `(f_2 - f_1)/f_1 xx 100`

= `(f_2/f_1 - 1) xx 100 = (13/10 - 1) xx 100`

= 30%

So, frequency increases by 30%.